Odvození rovnice postupné vlny

Z

rychlost

M 

M

On - Off

Reset

výsledná vlna

Z: y=y_msin ωt

=

M: y=y_msin(ωt-φ_0)

=y_msin(ωt-\omega t_0)

⇒

=

=y_msin(\frac{2\pi}{T}·t-\frac{2\pi}{T}·t_0)

=y_msin2\pi(\frac{t}{T}-\frac{t_0}{T})

=y_msin2\pi(\frac{t}{T}-\frac{x}{cT})

⇒

M:y=y_msin2\pi(\frac{t}{T}-\frac{x}{\lambda})

O = (40, -10)
N = (0, -10)
h = Segment(N, O)
y_{m1} = 4 (slider from 1 to 5, step 1)
λ_1 = 40 (slider from 5 to 50, step 1)
t = 0 (slider from 0 to 120, step 0.001)
c = 2
ggg = If((c * t) ≤ 40, (c * t), 40)
T_1: λ_1 / c
f(x) = (y_{m1} * sin(((2 * 3.141592653589793) * (t / T_1 - x / λ_1))))
A: (0, f(0))
g = Function(f, 0, ggg)
A_1 = (0, 0)
a = Segment(A, A_1)
M = Point(h)
rych = 0.194 (slider from 0.05 to 0.5, step 0.001)
G = (0, 10)
H = (0, -8)
e = Segment(G, H)
F = Midpoint(G, M)
D' = Mirror(M, a_1)
l = Segment(M, D')
J = Intersect(g, l, (10, -4))
I: M + (0, 2)
u = Vector((H + I) / 2, I)
v = Vector((H + I) / 2, H)
D = (0, 10)
n = Vector(D, D + ((y_{m1} * cos(((2 * 3.141592653589793) * t / T_1))), (y_{m1} * sin(((2 * 3.141592653589793) * t / T_1)))))
r = Circle(D, y_{m1})
K: (x(M), 10)
c_1 = Circle(K, y_{m1})
u_1 = Vector(K, K + ((y_{m1} * cos(((2 * 3.141592653589793) * t / T_1))), (y_{m1} * sin(((2 * 3.141592653589793) * t / T_1)))))
v_1 = Vector(K, K + ((y_{m1} * cos(((2 * 3.141592653589793) * t / T_1) - ((2 * 3.141592653589793) * Distance[H, I] / λ_1))), (y_{m1} * sin(((2 * 3.141592653589793) * t / T_1) - ((2 * 3.141592653589793) * Distance[H, I] / λ_1)))))
i_1 = If((c * t) ≤ 20, (c * t), 20)
x_1 = Distance(H, I)
text8: "c = " + c
B = Intersect(l, i)
text5: "x = " + x_1
text6: "Tau =  \frac{ x }{ c} = " + (x_1 / c)
on = 0
C = Intersect(c_1, l)
E = Intersect(r, e)
b = Segment(M, C)
L = Point(v)
j = Vector(M, M + (3, 0))
m = Vector(M, M + ((-3), 0))
p = Segment(J, (x(J), 0))
w = Vector(K, K + (y_{m1}, 0))
P = (0, -10)
mnohoúhelník1, q, s, d_1, e_1 = Polygon((0, -6), (10, -6), (10, 6), (0, 6))
d = Segment(P, E)
mnohoúhelník2, f_1, g_1, h_1, j_1 = Polygon((10, -6), (20, -6), (20, 6), (10, 6))
mnohoúhelník3, k_1, l_1, m_1, n_1 = Polygon((20, -6), (30, -6), (30, 6), (20, 6))
mnohoúhelník4, p_1, q_1, r_1, s_1 = Polygon((30, -6), (40, -6), (40, 6), (30, 6))
t_0: x_1 / c
Q: K + v_1
R: K + u_1
t_1 = CircleSector(K, Q, R)
S: K + w
c_2 = CircleSector(K, S, R)
fi_0: ((2 * π) * t_0 / T_1)
k: (16 * t_0 / T_1)
cc: c_1
text7: "T = " + T_1 + ""
text4: "λ = c T = " + λ_1 + ""
text11: "\varphi_0=\omega· t_0=\frac{2 \pi }{T}·t_0=\frac{ " + (LaTeX[k]) + "}{8}·\pi"
text9: "t_0=\frac{x}{c}=" + (LaTeX[t_0]) + ""